Examples: Putting terms in a commutative expression in the right order helps a lot even though “logically” it makes no difference. Align key symbols in formulae vertically on the page to group analogous clauses to make it clear what the next step is.
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Einstein notation replaces enormously complicated algebraic work with visually simple sub/superscript fiddling that analogizes kinesthetically to physically moving things around by hand. Also uses visually different symbols to track vector dimensions. https://en.wikipedia.org/wiki/Einstein_notation …pic.twitter.com/oBfWkyENZR
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Two quotes here from
@cdutilhnovaes about this. Also two of her key sources, which I haven’t yet looked into myself (but intend to).pic.twitter.com/CqSK3SAcna
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“The materiality of mathematics: Presenting mathematics at the blackboard” by
@greiffenhagen makes this much more concrete, through close study of a video of a lecturer presenting a proof of the completeness theorem for propositional logic.pic.twitter.com/Ru0J6xGfmz
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David Chapman Retweeted David Chapman
Here’s
@greiffenhagen showing the embodied, spacial, temporal, interactive nature of a proving of the Dutch Book Argument (cc@cdutilhnovaes)https://twitter.com/Meaningness/status/1005489362052632578 …David Chapman added,
David Chapman @MeaningnessStartling serendipity: I began a literature search on the ethnomethodology of formal rationality yesterday, and one of the first things to turn up was a video analysis of someone delivering the Dutch Book Argument! http://www.qualitative-research.net/index.php/fqs/article/view/1172/2585#g232 … pic.twitter.com/L7LoK6t85tShow this thread1 reply 0 retweets 8 likesShow this thread -
(Going to pick up this unfinished thread tomorrow probably—have other things to do now!)
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Replying to @Meaningness
Super interesting thread! When I teach programming, I force people to read and write everything out, to prevent them trying to "think it through" in their heads before their brains are trained to do this properly. So, on one hand, this aligns perfectly with that. 1/2
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Replying to @MissQuickstep @Meaningness
On the other hand, after >20 years programming, I can read, write, complie, execute and debug in my head with tremendous accuracy. My brain has gained the unconscious ability to suppress the "cognitive coloring" and interpret as the machine does. 2/3...
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Replying to @MissQuickstep @Meaningness
Interestingly, I didn't use two-step reasoning ("suppression of stage 1") for the 3 questions - the answers were immediately clear. So anecdotally, my experience is that while untrained brains suck at this kind of reasoning, it is a capability that can be developed (over decades)
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Yes, I had the same experience. I do think this is a learned capacity. Your idea that programming develops it better than math seems plausible to me (as someone who has done a lot more programming than math!)
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